COOLAIR and PRC2 function in parallel to silence FLC during vernalization

Significance The role of noncoding transcription in chromatin regulation is still controversial, extending to the role of transcription of antisense transcripts called COOLAIR in the Polycomb-mediated epigenetic silencing of Arabidopsis FLC (FLOWERING LOCUS C), a key step during vernalization. Here, we show that COOLAIR transcription and PRC2 (Polycomb Repressive Complex 2) silence FLC in parallel pathways: an antisense-mediated transcriptional repression capable of fast response and a slow PRC2 epigenetic silencing, both of which are affected by growth dynamics and temperature fluctuations. These features explain the varied importance of COOLAIR transcription in cold-induced FLC epigenetic silencing seen in various studies using different conditions. The parallel repressive inputs and extensive feedbacks make the mechanism counterintuitive but provide great flexibility to the plant.


Growth conditions
Seeds were surface sterilized and sown on 1x Murashige and Skoog (MS) media without glucose.As FLC shutdown in cold is sensitive to growth, seeds for expression analysis were sown at low density.Seeds were stratified for 2-3 days at 4ºC and grown for 10 days under long-day conditions (16h light, 8h dark at 20ºC).
For vernalization treatment, seedlings were transferred to short-day conditions (8h light, 16h darkness at constant 5ºC) after 10 days pre-growth.Plants harvested 10 days after vernalization were transferred back to long-day conditions and harvested from plates.For longer post-vernalization treatment (more than 10 days), the plants were transferred to soil and grown under long-day conditions.Fluctuating cold conditions used in Fig. 3 were as described previously (1).

Expression analysis
Total RNA was extracted using the hot phenol method as described previously (6).Genomic DNA contamination was removed with TURBO DNase (Invitrogen), following the manufacturer's guidelines.cDNA was synthesized with SuperScript IV reverse transcriptase (Invitrogen).Gene-specific primers were used for reverse transcription (RT) of COOLAIR, FLC, and VIN3.For the RT reaction to analyse the expression of vernalization factors in SI Fig. 1, oligo(dT) primers were used.Quantitative PCR (qPCR) was performed using SYBR Green I Master (Roche) and analysed on a LightCyler 480 machine (Roche).Ct values were normalized to the geometric mean of UBIQUITIN CARRIER PROTEIN 1 (UBC) and SERINE/THREONINE PROTEIN PHOSPHATASE 2 A (PP2A).All primers are listed in SI Appendix, Table S1.

Chromatin Conformation Capture
Chromatin conformation capture was performed as described previously (8,9) with minor modifications. 1 g of 10 days old seedlings were crosslinked in 2 % formaldehyde for 20 mins.Crosslinking was stopped by the addition of 2M Glycin to a final concentration of 0.125 M and vacuum infiltrated for 7 mins.Nuclei were extracted with Honda buffer as for ChIP (7).After purification, chromatin was digested with 600 U of BamHI (NEB) and BglII (NEB) for 14-16 h, followed by 8h of ligation with T4 ligation (Promega) at 17°C.DNA was purified with Phenol:Chloroform:IAA (25:24:1) and precipitated with isopropanol.DNA was dissolved in water and further purified using the ChIP DNA Clean & Concentration (Zymo Research) kit, following the manufacturer's protocol.The 3C library was quantified as described previously (8).
The same primers were used to analyse TEX2.0, as the NOS sequence inserted in TEX2.0 contains no additional BglII or BamHI restriction sites.

Mathematical modelling
In this study we use mathematical modelling to dissect the complex interplay of Polycomb mediated silencing and antisense mediated repression involved in FLC regulation in the cold.The models used in this study are constructed within a framework we have previously developed and experimentally validated.This framework describes the dynamics of transcriptional shutdown and histone modification changes at the whole-plant level during cold-induced epigenetic silencing at FLC (10,11).Therefore, the assumptions used in these previous models are carried through into the models developed here.Many of these assumptions are directly based on experimentally established details, while the validity of others has been established through experimental testing of model predictions in these previous studies (10,11).The models developed in this study use these assumptions as a starting point before we add additional features.

H3K36me3 and H3K27me3 dynamics in COOLAIR defective mutants
Our previously developed (and experimentally validated) models successfully captured the behaviour of H3K27me3 at FLC in cold and post-cold conditions observed in ColFRI, nucleation mutants, spreading mutants, as well as reactivation in a natural variant of FLC.These models also captured some, although not all, aspects of H3K36me3 dynamics.However, these models did not capture the role of antisense mediated regulation.Here, we start with the existing modelling framework, and attempt to build a model that, in addition to what is captured by previous models, can also properly incorporate the dynamics of H3K36me3 and H3K27me3 at FLC as observed in ColFRI and the COOLAIR defective mutants.To do this we focus on only those trends which are consistent across the three different COOLAIR defective mutants.These features are as follows (Fig. 2): 1. Similar dynamics of H3K27me3 nucleation and spreading in ColFRI and COOLAIR defective mutants, with a significant difference in starting (NV) levels.
• H3K27me3 nucleation is not slower in COOLAIR defective mutants.
• H3K27me3 levels at 6WT0 are similar in ColFRI and COOLAIR defective mutants.
• H3K27me3 spreading is similar in ColFRI and COOLAIR defective mutants.
2. Significant differences in H3K36me3 dynamics of the COOLAIR defective mutants during the cold.
• H3K36me3 increases across the locus (relative to NV) in the COOLAIR defective mutants in the first two weeks of cold, while ColFRI does not show this trend.
• The overall reduction in H3K36me3 levels over six weeks of cold is clearly weakened in the COOLAIR defective mutants, so that they exhibit significantly higher levels of this modification across the locus at 6WT0.
• Consistent with H3K36me3 changes and the association of this modification with transcription, FLC unspliced also reduces more slowly in the COOLAIR defective mutants.
3. Similar behaviour of H3K36me3 in COOLAIR defective mutants and in ColFRI during post-cold growth.
• A clear reduction of H3K36me3 levels is observed between 6WT0 and 6WT10/T20, in both COOLAIR defective mutants and ColFRI.
• Consistent with H3K36me3 reduction, and the association of this modification with transcription, FLC transcriptional output also reduces further in the post-cold.

Building a model to capture the differences in H3K36me3 dynamics
The behaviour of H3K27me3 in the COOLAIR defective mutants (described above) can be captured by previous models, since the behaviour is similar to ColFRI, except for the difference in NV levels.However, these models cannot capture the H3K36me3 behaviour, which shows significant differences in the COOLAIR defective mutants.This is because: (i) these models do not explicitly include a regulatory role for antisense transcription, and (ii) these models treat H3K36me3 and H3K27me3 as being exclusively present in different states of the FLC locus (H3K36me3 only in a high transcriptional state, and H3K27me3 only in a nucleated or spread state).

Capturing FLC states at the whole plant level
The existing modelling framework describes FLC locus states in a population of cells representing the whole plant.This population is made up of dividing and non-dividing cells (10,11).One of the core assumptions of these models is that the FLC locus can undergo nucleation of H3K27me3 in both dividing (meristematic tissue) and non-dividing cells.The validity of this assumption is supported by both direct and indirect experimental evidence: (i) for dividing cells, measurements of FLC epigenetic silencing by Polycomb in root meristematic cells via fluorescent imaging of FLC-Venus in plants defective for spreading of H3K27me3 ( 12); (ii) for non-dividing cells, the direct measurement of H3K27me3 nucleation by ChIP in mature leaves during vernalization in ColFRI (13); (iii) for non-dividing cells, the indirect evidence from all of our own ChIP time course datasets for H3K27me3: If only copies in dividing cells were capable of nucleation, the repeated division of these nucleated copies during rapid post-cold growth would cause a significant increase in population-level nucleation region H3K27me3.The fact that no such increase is observed by ChIP during post-cold growth indicates that FLC copies in both dividing and non-dividing cells can nucleate.This continues to be a core assumption in the models built here.As discussed in the main text, our data indicates that the antisense mediated repression and the PRC2/H3K27me3 mediated silencing function in parallel at FLC.This paradigm of two parallel pathways is therefore also central to the models developed here.

Possible models with different behaviour in subpopulations of cells
With the previously observed mutual exclusivity of H3K27me3 and H3K36me3 at FLC during vernalization (14), as well as other evidence for the mutual exclusivity of these modifications (15), it is tempting to consider models where apparent disruption of this mutual exclusivity in COOLAIR defective mutants arises from different subpopulations of FLC copies ending up in different states.While some tissue specific behaviour cannot be ruled out, here we examine two simple models with different behaviour between subpopulations and demonstrate that such subpopulation specific behaviour by itself is insufficient to capture the observed trends.

Model 1:
A simple approach to explain the difference in H3K36me3 dynamics during the cold between ColFRI and the COOLAIR defective lines, using the existing models, would be to introduce a subpopulation of cells only in the COOLAIR defective mutants, in which H3K27me3 does not nucleate at FLC in the cold.
These FLC copies would remain in an active transcriptional state, thus producing a higher level of H3K36me3 during the cold in the COOLAIR defective lines.However, the presence of such a nonnucleating subpopulation would be expected to produce a clear reduction of nucleation region H3K27me3 levels (compared to ColFRI) during the cold.Since this is not observed, particularly at 6WT0, we reject this model.

Model 2:
A more sophisticated model to explain the difference in H3K36me3 dynamics in the cold is one where we again have a subpopulation of non-nucleating cells, but this subpopulation is common to both ColFRI and the COOLAIR defective mutants.This subpopulation has to include roughly the same proportion of dividing cells as the rest of the population (otherwise this model would produce a post-cold increase in nucleation region H3K27me3, which as discussed above, is inconsistent with all our data).The existence of such a subpopulation would allow H3K27me3 dynamics to be unchanged between these genotypes.The higher H3K36me3 in the COOLAIR defective mutants could then be explained by antisense mediated repression having a role specifically in the non-nucleating subpopulation.However, since the non-nucleating population includes dividing cells, their active FLC states (and hence high H3K36me3 levels) would be maintained and propagated during post cold growth.Therefore, without invoking additional, unknown mechanisms for H3K36me3 removal in this subpopulation of cells, even this model cannot explain the post cold reduction in H3K36me3 leading to essentially the same levels in ColFRI and the COOLAIR defective mutants by 6WT10.Thus, we are led to construct a model where H3K27me3 and H3K36me3 can co-exist at the same FLC copy, and where antisense transcription mediated repression can modulate sense transcription associated H3K36me3 levels.We note that the coexistence of the two marks could potentially involve coexistence on the same H3 tail -H3K27me3 accumulation at FLC during cold is mediated by a VRN2-PRC2 complex, whose activity has been shown to be insensitive to the presence of H3K36me3 on a substrate H3 tail (15).
To capture the rapid response of this pathway observed under fluctuating temperatures (1), our model also includes a fast timescale response capability for the antisense mediated repression pathway.The mathematical model is detailed below.

Model features
Chromatin states at FLC copies: The model allows each copy to be in one of three states: an active transcriptional state (no H3K27me3 nucleation), an H3K27me3 nucleated state, and an H3K27me3 spread state.Importantly, the model also allows H3K36me3 to be present at the locus in all of these states, at a level that is determined by the transcriptional activity possible in each state rather than direct mutual exclusivity with H3K27me3.This means that the FLC copies in the active transcriptional state (no H3K27me3 nucleation) make the highest contribution to population level H3K36me3 levels; copies in the H3K27me3 nucleated state have lower transcriptional activity and hence make an intermediate contribution to population level H3K36me3; copies in the H3K27me3 spread state have the lowest transcriptional activity and hence make the lowest contribution to population level H3K36me3.We note that the above features replace the assumptions used in previous models (10,11) : (1) Allowing H3K36me3 to be present in all states at a level determined by transcriptional activity replaces the previous assumption that this modification is only present in a high transcriptional state of FLC.
(2) Having only three states of the locus -active, H3K27me3 nucleated, and H3K27me3 spreadreplaces the assumption that there is a distinct, "inactive" state of the locus with neither H3K36me3 nor H3K27me3 accumulation, which is set up by a "VIN3 independent" pathway.
The new assumptions allow the model to capture transcriptional downregulation and H3K36me3 levels in parallel to H3K27me3 mediated changes of transcriptional state, and thus emphasises the paradigm that emerges from our data -that of parallel pathways (antisense transcription mediated and PRC2 mediated) converging to regulate FLC expression.

Dividing and Non-dividing loci:
The total number of dividing copies is fixed.We use a simplified division model (11), where each division produces one dividing copy and a fixed number of non-dividing copies.

Nucleation and Spreading:
• Transitions from an active to a nucleated state are allowed only in the cold, with the probability of nucleation dictated by the VIN3 protein concentration calculated from the LSCD model of VIN3 dynamics ( 10) -a predictive model of VIN3 expression that captures the effect of multiple thermosensory inputs operating at different timescales.
• The transition from a nucleated to a spread state occurs during replication/division, consistent with the dependence of spreading on an active cell cycle that we have previously shown (12).
• Replication/division causes a transition from a nucleated to a spread state: each division of a nucleated copy produces one dividing, spread copy and a fixed number of non-dividing, spread copies.
• The spread state is assumed to be stable -the model does not allow reactivation from the spread state.
• Except in simulations of the spreading mutant, we assume no loss of nucleation at nucleated, dividing copies.

Division rate and pre-growth duration
• The growth rate is assumed to undergo a step change in the cold (5℃) conditions -reduced by a factor of 40 relative to warm (22℃) conditions (11).
• The step change of growth rate is assumed to be the same in constant cold and fluctuating temperature conditions.
• The pre-growth duration is fixed at 10 days (11).

Sense transcriptional activity (initiation rate): Antisense mediated regulation of sense transcription
(initiation rate) is assumed to be possible in the active and nucleated states.The highest level of transcriptional activity in the nucleated state is assumed to be 0.3 of the highest level in the active state.
Based on our data, which shows that cold induced H3K27me3 nucleation and post-cold H3K27me3 spreading are not disrupted in the COOLAIR defective mutants, we assume that nucleation and spreading of H3K27me3 (i.e., the rates of transition to these states) are unaffected by the absence of the antisense mediated repression.

Sense transcriptional activity (PolII speed):
The increase in H3K36me3 between NV and 2WT0 observed in the COOLAIR defective mutants cannot be captured by only having co-transcriptional addition of this modification -there is a general trend towards reduction rather than an increase in sense transcriptional activity between these timepoints (as measured by FLC unspliced and spliced transcript levels).Therefore, to capture this increase in H3K36me3, we introduce a reduction in the speed of RNA PolII in the nucleation region in the cold: it is assumed to undergo a step change drop to 0.6 of its NV value in the cold and also recovers post-cold.Such a reduction in Pol II speed in the nucleation region allows the Pol II dwell time to increase between the NV and 2WT0 timepoints, even with a reduction in transcriptional activity (initiation rate) between these timepoints.We assume that the same reduction in PolII speed in the nucleation region also occurs under the fluctuating temperature conditions.

Antisense mediated (nucleation independent) repression pathway: A nucleation independent repression
pathway performs analogue control of the sense transcription level in active and nucleated states.The functioning of this pathway is assumed to rely on antisense (AS) transcription (i.e., this pathway is not functional in the COOLAIR defective mutants).

Slow timescale component: Under cold conditions, both constant and fluctuating cold, repression
by the AS pathway is assumed to increase slowly in the cold and decrease quickly upon return to warm, consistent with NTL8 dynamics (16).The repression is modelled as a slow reduction in the sense transcription initiation rate in the cold, and a rapid recovery in the initiation rate in the postcold.This is captured by a multiplicative factor set to vary between 1 and 0.5 with an exponential decay over time in cold and a faster exponential recovery over time in the warm (see model implementation below).This is consistent with our previous model-predicted NTL8 accumulation dynamics determined by slower growth in the cold (16), and rapid NTL8 reduction during postcold growth, as well as the measured slow build-up of FLC antisense transcripts in constant cold measured by qPCR (17) This is also consistent with the analysis of the VIN3 independent pathway in (10) -the dynamics of this pathway was predicted to be temperature dependent, causing slow FLC reduction in the cold, but allowing rapid increase in the post cold in the absence of VIN3 dependent H3K27me3 nucleation.The reduction of the transcriptional initiation rate (caused by the AS pathway) is assumed to have the same dynamics at active (non-nucleated) and nucleated copies.
The transcriptional initiation recovery timescale in the post-cold is also assumed to be the same at non-nucleated and nucleated copies.

Fast timescale component:
To capture the rapid response of the antisense mediated repression under fluctuating temperature conditions, we assume that low temperatures cause a large reduction in the sense transcription initiation rate (due to strong upregulation of antisense transcription).
While freezing temperatures are seen to have the strongest effect on upregulating antisense transcription, we note that in our experimental data, both mild and strong fluctuating conditions cause significant downregulation of FLC sense transcription, with the reduction of both FLC mRNA and H3K36me3 being largest in FS conditions and intermediate in FM conditions.To capture these effects in both FM and FS conditions, we assume a simple step change in the antisense mediated repression.This is represented by the multiplicative factor defined above undergoing a step reduction to a value of 0.05 whenever the temperature falls below 4℃.Above this temperature, this factor takes a slow, exponentially decaying value (as a function of time) as described above (see Table S1 for definition).
Thus, under fluctuating temperature conditions we assume that, in addition to the large step changes to the multiplicative factor, a slow timescale reduction in this factor also occurs.Not including a slow timescale reduction under fluctuating conditions would cause the model to fail in capturing the observed changes to H3K36me3 and FLC mRNA under FM and FS conditions.Note that the reduction in Pol II speed in the nucleation region assumed for constant cold is also assumed to occur under FM and FS conditions.In the absence of this assumption -i.e., if the PolII speed is assumed to change only in constant cold conditions -the model would predict even larger changes in H3K36me3 under FM and FS conditions relative to NV.
We note that the above set of assumptions describing the antisense mediated pathway replaces population level H3K36me3 in the simpler description of a "VIN3 independent" pathway used in our previous models (10,11).

H3K27me3 levels:
The contribution to H3K27me3 levels from an individual FLC locus depends on the state of the locus: low in the nucleation region (NR) and non-nucleation region (body) for active copies, high in the NR and low in the body for nucleated copies, high in the NR and body for spread copies.

H3K36me3 levels in the NR depend on Pol II density:
For simplicity, the model describes the population level average H3K36me3 levels in the FLC nucleation region, but we note that the levels of this modification across the gene body follow the trends in the nucleation region in all our data (Fig. 2B, (12,14)), with the only exception being the 3' end of the locus, where H3K36me3 levels reflect the level of antisense transcription (increasing during the cold (Fig. 3A,C), (14) and high in ntl8-D3 (Fig. 1B)).
H3K36me3 is represented as a dynamical variable in the model, and based on the above evidence, the rate of addition of H3K36me3 is assumed to be proportional to the Pol II density.This is consistent with cotranscriptional addition of this modification (18), as well as longer Pol II dwell time at a given location allowing a greater window of opportunity for adding this modification (19).The Pol II density is determined by the ratio of initiation rate to PolII speed in the nucleation region.As described above, the initiation rate is determined by two factors -the H3K27me3 state and the antisense mediated repression pathway -while the PolII speed undergoes a step change in cold conditions.We also assume a constant turnover rate of H3K36me3 -the value of the rate constant is assumed to be 1.21  !" , consistent with the half-life of H3K36me2 (0.571 day) estimated in (20), since no data was available for H3K36me3.
FLC mRNA level: The model describes the population level average FLC mRNA level as a dynamical variable, whose production is determined by the sense transcription initiation rates of the FLC copies in different states.As described above, these initiation rates are also determined by the antisense mediated repression.We fix a turnover rate for FLC mRNA consistent with a half-life of 6 hr as estimated in (21).
Fluctuating temperature input to the model: The temperature profiles used to simulate FM and FS conditions are shown in Table S2.We note that in the model, based on the above assumptions, this dynamic temperature input is affecting two components -the antisense mediated repression (as described above) and the LSCD model of VIN3 dynamics (thus determining the nucleation rate) (10).Other temperature dependent rates -Pol II elongation and growth -are assumed to undergo a step change in the cold, so they are not affected by other dynamics of the temperature input.

Model implementation
Following the same approach as for our previous models (10,11), an ODE (Ordinary Differential Equation) model is constructed using the above assumptions.The model equations are shown below.The model is simulated using the ode15s solver in Matlab version 2017a.

Model Variables:
(fraction of active, dividing copies) (fraction of nucleated, dividing copies) (fraction of spread, dividing copies) (ratio of active, non-dividing copies to total number of dividing copies) (ratio of nucleated, non-dividing copies to total number of dividing copies) (ratio of spread, non-dividing copies to total number of dividing copies) The dynamics are such that at all timepoints.

Basic Model (representing ColFRI):
Here, the total fractions of copies in each state (at any timepoint), i.e.,  # ,  $ ,  % , can be computed as follows: Total fraction of active copies: Total fraction of nucleated copies: Total fraction of spread copies: Here, () represents the division rate, which undergoes a step change reduction in the cold.g(T) is assumed to undergo a step reduction under FM and FS conditions, exactly as under constant cold conditions.
The step change (factor of 40) is assumed to be the same under all three conditions.represents the nucleation rate, computed using the VIN3 level as in (11), where the VIN3 level is itself computed using the LSCD model (10).At all timepoints, the current temperature is an input to the LSCD model.
represents the number of non-dividing copies produced at each division event (using the same simplified description as in (11).
The rate of addition of H3K36me3 is assumed to be proportional to the function  &'( ( # ,  $ ,  % ): . The time-dependent multiplicative factor () captures the repression by the antisense mediated pathway.
This factor has a basal value of 1 and decays exponentially with time to 0.5 in the cold and recovers exponentially with time in the post-cold.() undergoes a step reduction to a value of 0.05 whenever the temperature falls below 4℃.When the temperature subsequently rises above 4℃, () returns to its slow decaying value, which decays continuously irrespective of the temperature fluctuations.
Note that having the parameter  $ > 0 above means that copies in an H3K27me3 nucleated state can also contribute to H3K36me3 addition.This reflects the model assumption that these two modifications can coexist in the nucleation region at a single FLC copy during cold induced silencing, with the H3K36me3 levels being limited only by the level of sense transcription.This assumption is based on the ability of the VRN2-PRC2 complex (which mediates cold induced H3K27me3 accumulation at FLC) to methylate H3 histones even when they carry K36 methylation (15).
We describe FLC mRNA as an additional dynamical variable, whose production rate is proportional to Model for COOLAIR defective mutants: For simulating the COOLAIR defective mutants, the same model is used, but with the antisense mediated pathway assumed to be non-functional.This is captured by setting () = 1 throughout the simulation.

Model for H3K27me3 Nucleation mutants:
The basic model is used with the nucleation rate set to zero throughout the simulation.The initial conditions in this case are still allowed to have a non-zero fraction of H3K27me3 spread FLC copies, consistent with the NV level of H3K27me3 observed in cold-nucleation mutants including vrn2-1 and vin3-4 (12).

Model for H3K27me3 Spreading mutant:
Here we modify the basic model to capture reactivation/loss of H3K27me3 nucleation.At each division event, a nucleated dividing copy is allowed to undergo three different scenarios (11): • Reactivation, producing one active dividing copy and active non-dividing copies.
• Spreading, producing one spread dividing copy and spread non-dividing copies.
Here represents the fraction of nucleated dividing copies undergoing reactivation and represents the fraction of nucleated dividing copies undergoing spreading, at each replication/division event.
The parameters  $01 ,  %23, , and  3+#14 were computed numerically (see SI Table 1 of parameter values), using a Monte-Carlo approach to carry out five successive replication/division events starting from one nucleated copy (five divisions is consistent with our assumption of  $ = 32 (11)).

Processing simulation output:
The total fractions of copies in each state (at any timepoint) can be computed as follows from the simulation output: Total fraction of active copies: Total fraction of nucleated copies: Total fraction of spread copies: The total fractions of copies in each state are then used to compute the H3K27me3 levels as follows: NR H3K27me3 level: Body H3K27me3 level: The factor  &56 is used for scaling the model output for comparison to ChIP-qPCR data.Similarly, a factor  &'( is multiplied when comparing H3K36me3 levels to the ChIP-qPCR data.

Comparing model predictions to experimental data under fluctuating temperature conditions:
In Figure S11(B,C,D), we compare the model predicted H3K36me3, H3K27me3, and FLC mRNA levels for ColFRI at the 2WT0 timepoint under fluctuating conditions to experimental data.
The model assumes that the FLC transcriptional shutdown in fluctuating conditions is mediated mainly by an enhanced antisense pathway.Hence, in the case of a COOLAIR defective mutant, this model would predict that the FLC transcriptional shutdown is mostly disrupted even in FM and FS conditions.Therefore, this model would predict an increase in H3K36me3 after 2W FM and FS conditions, similar to the increase predicted under constant cold conditions at the same timepoint (as shown in Figure 4).The experimental data for the TEX1.0FLClean mutant does show increased H3K36me3 across the locus under FM conditions (Fig. 3(D)).which is qualitatively consistent with the model prediction.This is similar to the increased H3K36me3 across the locus observed for all three COOLAIR defective mutants after 2W cold (Fig. 2(B)).
However, under FS conditions, the data shows a reduction in H3K36me3 (although this reduction is significantly attenuated compared to ColFRI -Figure S9F).This indicates that there may be additional factors driving the transcriptional shutdown under FS conditions that are not captured by this simple model, which require further experimental analysis of chromatin state changes under fluctuating temperatures to dissect.

Note: Defining parameter values under fluctuating temperature conditions
The instantaneous temperature input affects the parameters in the LSCD model of VIN3 dynamics and the rate of VIN3 mediated nucleation as described in (10).The parameter (), representing the antisense mediated repression undergoes step changes under the fluctuating temperature conditions as defined above.
(), representing the division rate and (), representing the Pol II speed in the nucleation region, are set to the same, constant value under all three cold conditions (constant, FM, FS).See Table S1 for details.
spread state.The perpetuated state not included since this state is not expected to play a major role in the phases of silencing examined in this study.This state can be incorporated into the current model for studying aspects such as post-cold FLC reactivation.NucleationTransition to nucleated state partly relies on transcriptional downregulation (i.e., prior transition to inactive state).
&'( ( # ,  $ ,  % ) represents the contribution to overall H3K36me3 addition from FLC sense transcriptional activity at FLC copies in different states, with the sense transcriptional activity dictated by both the H3K27me3 nucleation state (represented by , and  % ) and the antisense mediated repression (represented by ()).The multiplicative factors , and  % represent the maximum transcription initiation rate for active, nucleated, and spread copies respectively.() represents the Pol II speed in the nucleation region, which is assumed to undergo a step change (reduction) during the cold. &'(*+' , represents the turnover rate constant of H3K36me3.The H3K36me3 level is assumed to be normalised to its steady state level when  # = 1, () = 1, and () = 1 (i.e.,  &'( ( # ,  $ ,  % )=1).

Fig. S1 .
Fig. S1.Relative expression of other factors involved in vernalization.Expression of vernalization factors in ntl8-D3 FRI compared to ColFRI in non-vernalized conditions.Data are presented as the mean ± s.e.m (n ≥ 3).Asterisks indicate significant different (p ≤ 0.05, two-tailed t test).n.s, not significant.Each open circle represents a biological replicate.

Fig. S2 .
Fig. S2.Constitutive expressed VIN3 binds the nucleation region at FLC. (A) Schematic of the construct used to generate transgenic lines that express VIN3 in the absence of cold.The VIN3 promoter was exchanged with the promoter sequence of VRN5 (pVRN5).(B) Expression of VIN3 in non-vernalized conditions (NV), VIN3 expression in ColFRI after six weeks of vernalization (6WT0) is shown for comparison.Data are presented as the mean ± s.e.m relative to the geometric mean of PP2A and ACTIN.Each open circle represents a biological replicate.The numbers under the bars refer to individual transgenic lines.(C) VIN3-eGFP ChIP-qPCR enrichment at FLC at NV. Data are shown as percentage input.Non-transgenic ColFRI plants were used as a negative control sample.Error bars represent mean ± s.e.m. (n = 3 biological replicates).

Fig. S3 .
Fig. S3.Gene-loop is disrupted in TEX2.0.Quantitative 3C over the FLC locus in 10-day-old ColFRI and TEX2.0 flclean FRI with BamHI and BglII (similar to Fig.1G).A schematic of the TEX2.0 transgene is shown above.BamHI and BglII restriction sites are indicated with dotted lines, and the respective regions are numbered with Roman numerals.The insertion of the NOS sequence does not result in additional 3C fragments when assayed with BglII and BamHI.Red arrows indicate the primers' location for 3C-qPCR.The region around the FLC transcription start site was used as the anchor region in the 3C analysis.The data shows the relative interaction frequencies (RIF) and are the average of at least seven biological replicates.Data are presented as the mean ± s.e.m. (n ≥ 7).The midpoint of the assayed 3C fragments is plotted.

Fig. S5 .Fig. S6 .
Fig. S5.Quantitative analysis of antisense role in histone modification dynamics.All comparisons shown consist of comparing the mean levels over three nucleation region primers between ColFRI to each of the defective COOLAIR lines (See supplementary information for details of primers).In cases where the qualitative trends were clear and consistent across the three defective COOLAIR lines, a one-tailed Student's t-test was used for each comparison.Error bars represent s.e.m. (n = 3 biological replicates).In (A), where there was no clear trend, a two-tailed Student's t-test was used.In all cases, the Bonferroni correction was used to adjust the significance level from  = 0.05 to  = 0.0167 (for three comparisons).(*) indicates P < 0.0167 ; ns indicates no significance (P ≥ 0.0167).(A) Fold change (increase) of H3K27me3 in the nucleation region during first 2 weeks of cold treatment (2WT0/NV) is not significantly different between ColFRI and the defective COOLAIR lines.(B) Fold change (increase) of H3K27me3 in the nucleation region during the 2WT0 to 4WT0 period is significantly higher in the COOLAIR lines.(C) H3K27me3 levels at 6WT0 are not significantly lower in the defective COOLAIR lines.(D) NV level of H3K27me3 in the nucleation region is significantly higher in ColFRI.(E) FLC expression in 10 days old seedlings before cold exposure in ColFRI and the three defective COOLAIR lines; TEX1, TEX2, and FLC∆COOLAIR.Unspliced RNA was measured and is shown relative to UBC and ColFRI.Error bars represent s.e.m. (n = 3 biological replicates).(F-G) Similar analysis as in (A-D).NV level of H3K36me3 is not significantly higher in the defective COOLAIR lines (F).The fold change in H3K36me3 over 6W of cold treatment indicates significantly smaller changes in H3K36me3 in the defective COOLAIR lines (G).

Fig. S9 .
Fig. S9.Fold change comparisons for changes in nucleation region H3K36me3 andH3K27me3.This analysis is based on ChIP-qPCR time course data presented in Figs.1,2.Error bars represent mean ± s.e.m. (n ≥ 3).All comparisons shown consist of comparing fold changes in the mean levels over three nucleation region primers in the indicated genotypes between different periods of cold and non-vernalized conditions (see supplementary information for details of primers).In all cases, the data showed clear trends, so a one-tailed Student's t-test was used for each comparison.In (A-C) and (F), a significance level of alpha = 0.05 was used.(*) indicates P<0.05; ns indicates no significance (P≥0.05).In (D), the Bonferroni correction was used to adjust the significance level from alpha = 0.05 to alpha = 0.025 (for two comparisons).ns indicates no significance (P≥0.025).In (E), the Bonferroni correction was used to adjust the significance level from alpha = 0.01 to alpha = 0.005 (for two comparisons).(**) indicates P<0.005; ns indicates no significance (P≥0.005).(A) Comparison of NR H3K36me3 fold changes after 6 weeks cold (6WT0) in ColFRI and vrn2-1.(B) Comparison of NR H3K27me3 fold changes after 2 weeks cold

Figure S10 .
Figure S10.Model predictions of impact of vernalization mutants on histone dynamics.(A-D) Time course predictions from the mathematical model for other vernalization mutants: anH3K27me3 nucleation mutant, and a spreading mutant.The predictions are compared to previously published ChIP-qPCR time course data presented in(12).
Caption for Figure S11: Fast timescale response of the antisense mediated repression pathway to temperature fluctuations can capture experimentally observed changes under fluctuating temperature conditions.(A) Temperature profiles used in the fluctuating temperature experiments.(B) Comparison of experimentally measured (left) and model predicted (right) changes in FLC transcriptional output in ColFRI after 2W constant cold (CC), 2W fluctuating mild (FM), or 2W fluctuating strong (FS) conditions.The experimentally measured levels are normalised to the mean NV level.(C) Comparison of experimentally measured (left) and model predicted (right) changes in nucleation region H3K36me3 in ColFRI after 2W constant cold (CC), 2W fluctuating mild (FM), or 2W fluctuating strong (FS) conditions.(D) Comparison of experimentally measured (left) and model predicted (right) changes in nucleation region H3K27me3 in ColFRI after 2W constant cold (CC), 2W fluctuating mild (FM), or 2W fluctuating strong (FS) conditions.

Table S1 .
Model parameter values

Table S2 .
Fluctuating temperature profiles input to model (matching conditions used in fluctuating temperature experiments).The temperature input is linearly interpolated between the hourly timepoints shown.List of primers used in this study.